On the shape and size of granular roll waves

This paper describes, from a theoretical point of view, the appearance and characteristics of granular roll waves in chute flow, and the maximal size these waves can attain for a given influx of material into the system. Granular roll waves are steady travelling wave solutions of the generalized Saint-Venant equations for flowing granular matter, appearing when the Froude number Fr of the incoming flow exceeds a critical value, Fr > Fr-cr. We focus upon the phase space of the corresponding dynamical system, where the roll waves take the form of a stable limit cycle around an unstable fixed point; this limit cycle gives precise information on the size and periodicity of the roll wave. It is found that, for any given value of Fr, the limit cycle cannot become arbitrarily large because it is constrained by a homoclinic loop in phase space. Roll waves of larger amplitude can be generated by increasing the Froude number Fr.

Automated summary

This paper theoretically describes the appearance and characteristics of granular roll waves in chute flow, as well as the maximal size these waves can attain for a given influx of material. The paper finds that the size of the roll waves is constrained by a homoclinic loop in phase space, and larger amplitude roll waves can be generated by increasing the Froude number.